How to chain states when unfolding a stream?

[clintonmead]

So I've got a function like the following:

getOneToken :: (ByteString, State) -> Maybe (Token, (ByteString, State))
getOneToken = _ 

So what this does is grabs one Tokens slices a bit off the front of the ByteString (we can do this without copying with ByteString) and gives both a Token, and the remaining ByteString, plus some State.

We can then do:

unfoldBytestring :: Unfold m (ByteString, State) Token
unfoldBytestring = unfoldR getOneToken

But here's what I want to do. Lets say we have an incoming stream of bytestrings:

byteStringStream :: Stream m ByteString

What I want to do is state with an initial state say:

initialState :: State
initialState = _

and feed that into unfoldBytestring to get a stream of Tokens. But once that unfold returns Nothing, I want to use the same unfold to unfold the next ByteString in byteStringStream into a stream of Tokens, but this time instead seeding the unfold with initialState, I want to seed it with the last State returned from the previous fold (i.e. just before the previous unfold returned Nothing).

Note here the full "state" is (ByteString, State), so the second unfold I want to seed with the second ByteString in the unfoldBytestring along with the last State from the unfolding of the first ByteString in unfoldBytestring.

Is there a function/combinator to do this? Or should I write my own? It seems close to unfoldMany, I just need a way to collect the final states from the unfolds and pass them along. I think the signature I need is something like this:

unfoldManyChain :: ((s, a) -> s) -> (a -> s) -> Unfold m s b -> Stream m a -> Stream m b
unfoldManyChain nextStateFunc initialStateFunc unfold stream

Where we take the first element a from stream, apply initialStateFunc to it to get s, then unfold that s to get a stream of b, and continue by combining the last state s from the previous unfold with the next a from stream to get a new state s which we then use unfold to produce more elements and so on.

[shlok]

Turning Stream a into a Stream b using a given stateful computation (a Fold) is something I have been doing with scan or postscan. Will this not work for you?